Sorting in Data Structure: Categories & Types [With Examples]

The arrangement of data in a preferred order is called sorting in the data structure. By sorting data, it is easier to search through it quickly and easily. The simplest example of sorting is a dictionary. Before the era of the Internet, when you wanted to look up a word in a dictionary, you would do so in alphabetical order. This made it easy.

Imagine the panic if you had to go through a big book with all the English words from the world in a jumbled order! It is the same panic an engineer will go through if their data is not sorted and structured. 

So, in short, sorting makes our lives easier. Check out our data science courses to learn in-depth about data science algorithms.

In this post, we will take you through the different data structures & sorting algorithms. But first, let’s understand what a sorting algorithm is and sorting in data structure. 

Table of Contents

A sorting algorithm is just a series of orders or instructions. In this, an array is an input, on which the sorting algorithm performs operations to give out a sorted array.

Many children would have learned to sort in data structures in their computer science classes. It is introduced at an early stage to help interested children get an idea of deeper computer science topics – divide-and-conquer methods, binary trees, heaps, etc.

Here’s an example of what sorting does.

Let’s suppose you have an array of strings: [h,j,k,i,n,m,o,l]

Now, sorting would yield an output array in alphabetical order.

Output: [h,i,j,k,l,m,n,o]

Let’s learn more about sorting in data structure.

Checkout: Types of Binary Tree

Before delving into the different types of sorting in data structure, let’s first look at why sorting in data structure is important. Sorting in DSA actually provides users with several benefits. For example, when you are performing sorting on elements, many complications such as min/max, kth smallest/largest get automatically simplified. Furthermore, sorting also provides you with many algorithmic solutions, some of which might include divide and conquer, iterative, and recursive-based. 

Last but not least, perhaps one of the biggest benefits of sorting in DSA is time complexity. As a coder, the ultimate goal is to solve any kind of complex problem within the minimum amount of time. That is where different types of sorting in data structure  come into play. It not only saves up your very precious time but also provides you with the right solution. 

With that said, now lets’ take a look at the different sorting techniques in data structure. 

There are two different categories in sorting:

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Here are a few of the most common types of sorting algorithms.

This algorithm works on splitting an array into two halves of comparable sizes. Each half is then sorted and merged back together by using the merge () function.

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Here’s how the algorithm works:

MergeSort(arr[], l,  r)

If r > l

             middle m = (l+r)/2

             Call mergeSort(arr, l, m)

             Call mergeSort(arr, m+1, r)

             Call merge(arr, l, m, r)

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Check out the image below to get a clear picture of how this works.

Source

Python program for merge sort implementation

def mergeSort(a): 

    if len(a) >1: 

        mid = len(a)//2

        A = a[:mid]   

        B = a[mid:]

        mergeSort(A) 

        mergeSort(B) 

        i = j = k = 0    

        while i < len(A) and j < len(B): 

            if A[i] < B[j]: 

                a[k] = A[i] 

                i+=1

            else: 

                a[k] = B[j] 

                j+=1

            k+=1

        while i < len(A): 

            a[k] = A[i] 

            i+=1

            k+=1       

        while j < len(R): 

            a[k] = B[j] 

            j+=1

            k+=1 

def printList(a): 

    for i in range(len(a)):         

        print(a[i],end=” “) 

    print() 

if __name__ == ‘__main__’: 

    a = [12, 11, 13, 5, 6, 7]   

    mergeSort(a) 

    print(“Sorted array is: “, end=”\n”) 

    printList(a) 

Learn more: Recursion in Data Structure: How Does it Work, Types & When Used

In this, at first, the smallest element is sent to the first position.

Then, the next smallest element is searched in the remaining array and is placed at the second position. This goes on until the algorithm reaches the final element and places it in the right position. 

Look at the picture below to understand it better.

 Source

Python program for selection sort implementation

import sys 

X = [6, 25, 10, 28, 11] 

for i in range(len(X)): 

        min_idx = i 

    for j in range(i+1, len(X)): 

        if X[min_idx] > X[j]: 

            min_idx = j 

    X[i], X[min_idx] = X[min_idx], X[i]  

print (“The sorted array is”) 

for i in range(len(X)): 

    print(“%d” %X[i]),  

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It is the easiest and simplest of all the sorting algorithms. It works on the principle of repeatedly swapping adjacent elements in case they are not in the right order.

In simpler terms, if the input is to be sorted in ascending order, the bubble sort will first compare the first two elements in the array. In case the second one is smaller than the first, it will swap the two, and move on to the next element, and so on.

Example:

Input: 637124

First pass

637124 -> 367124 : Bubble sort compares 6 and 3 and swaps them because 3 367124 : Since 6 361724 : Swapped 7and 1, as 7>1

361724 -> 361274 : Swapped 2 and 7, as 2 361247 : Swapped 4 and 7, as 4 361247

361274 -> 316274

316274 -> 312674

312674 -> 312674

312674 -> 312647

Third pass

312647 -> 132647

132647 -> 123647

123647 -> 123647

123647 -> 123467

123467 -> 123467

As you can see, we get the ascending order result after three passes.

Python program for bubble sort implementation

def bubbleSort(a): 

    n = len(a) 

    for i in range(n): 

        for j in range(0, n-i-1): 

            if a[j] > a[j+1] : 

                a[j], a[j+1] = a[j+1], a[j]  

a = [64, 34, 25, 12, 22, 11, 90] 

bubbleSort(a) 

print (“The sorted array is:”) 

for i in range(len(a)): 

    print (“%d” %a[i]), 

Also read: Data Frames in Python: Python In-depth Tutorial

Insertion sort falls under one of the most popular sorting types in data structure. It is basically an algorithm that helps to place an unsorted element at its suitable position in each iteration. It’s similar to the way you sort your cards during a card game. The first card is usually considered to be already sorted, and the next card that you pick up is then compared against the first one. Based on the first card, you wither place the unsorted second card on the right or left side of the former one. The insertion sort follows the same approach.

Also known as partition exchange sorting, quick sort is yet another very popular sorting types in data structure that is based on partition. Using this particular algorithm, you pick on an element, which is known as the pivot element, and then rearrange the rest of the elements around the pivot element. It then further divides the array into two specific sub-arrays. Once you have fixed the pivot element, then it automatically disintegrates the rest of the elements. For example, elements that are lesser are placed on the left side of the pivot element, and elements on the right side are usually the ones that are greater. This whole process continues until only one element is left in the sub-array. 

With this, we come to an end of the different types of sorting techniques in data structure. As quite visible from the list, each DSL sorting has its own advantages and disadvantages. Therefore, while choosing the most efficient one, you need to first understand the need for your data. For example, if you are looking for something stable, you should go with the merge. Simultaneously, if you are constrained in space, heap sort is the perfect choice for you. 

That wraps up sorting in data structure and the most common sorting algorithms. You can choose any of the different types of sorting algorithms. However, remember that some of these can be a little tedious to write the program for. But then, they might come in handy for quick results. On the other hand, if you want to sort large datasets, you must choose the bubble sort. Not only does it yield accurate results, but is also easy to implement. Then again, it is slower than the other types. I hope you liked the article about sorting in data structure. 

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Different sorting techniques are utilized for performing the sorting procedures as per the requirements. Usually, Quick Sort is used as it is faster, but one would use Heap Sort when memory usage is the concern.

Heap Sort is a comparison-based sorting algorithm completely based on the binary heap data structure. This is why heap sort can take advantage of the heap’s properties. In the quick sort algorithm, the Divide-and-Conquer approach is utilized. Here, the entire algorithm is divided into 3 steps. The first one is to pick an element that acts as the pivot element. Next, the elements to the left of the pivot element are smaller ones and to the right are the bigger ones in value. On every partition, the previous step is repeated to sort the entire array of elements.

If you are dealing with sorting algorithms, then you will have noticed that Bubble Sort is the simplest one among all the others. The basic idea behind this algorithm is to scan the entire array of elements and compare every adjacent element. Now, the swapping action occurs only when the elements are not sorted.

With Bubble Sort, you just have to compare the adjacent elements, and the array gets sorted. This is why it is considered to be the simplest sorting algorithm.

Quicksort is considered to be the fastest one among all the other sorting algorithms. The time complexity of Quicksort is O(n log n) in its best case, O(n log n) in its average case, and O(n^2) in its worst case. Quicksort is known to be the fastest sorting algorithm because of its best performance in all the average case inputs. The speed will depend a lot on the amount of data too. As per the comparison between all the sorting algorithms, Quicksort is the fastest because of its average case inputs.